Covariant conservation equations and their relation to the energy-momentum concept in general relativity

1978 ◽  
Vol 18 (12) ◽  
pp. 4399-4407 ◽  
Author(s):  
T. N. Palmer
Keyword(s):  
General Relativity ◽  
Conservation Equations

scholarly journals The Boltzmann Equations in General Relativity

1936 ◽  
Vol 4 (4) ◽  
pp. 238-253 ◽  
Author(s):  
A. G. Walker
Keyword(s):  
General Relativity ◽  
Continuous Medium ◽  
Equations Of Motion ◽  
Free Particle ◽  
Energy Tensor ◽  
Principle Of Equivalence ◽  
Boltzmann Equations ◽  
Conservation Equations ◽  
Proper Mass ◽  
Conservation Of Momentum

In a recent paper, J. L. Synge gives an interesting derivation of the conservation equations Tij,j = 0 satisfied by the energy tensor Tij of a continuous medium. Previous to the appearance of this paper, these equations were generally obtained by assuming the classical equations of motion and continuity, after which it was necessary to appeal to the Principle of Equivalence. It then follows that the path of a free particle is a geodesic. Synge however starts with the hypothesis that the path of a particle between collisions is a geodesic and that the proper mass is constant. The conservation equations are then deduced exactly from the law of conservation of momentum for collisions.

XIX.—A Theory of Regraduation in General Relativity

1946 ◽  
Vol 62 (2) ◽  
pp. 164-174
Author(s):  
A. G. Walker
Keyword(s):  
General Relativity ◽  
Symmetric Space ◽  
Special Form ◽  
The Other ◽  
Spherically Symmetric ◽  
Conservation Equations ◽  
Interesting Paper ◽  
Equivalence Theory ◽  
Two Alternatives

1. It was remarked by me a few years ago that temporal regraduations, other than trivial changes of zero and unit, had not so far been considered in General Relativity. An interesting paper by Dr G. C. McVittie has now appeared in which regraduations are examined in certain spherically symmetric space-times. Under the assumptions made by McVittie it is shown that regraduations can exist for some but not all space-times, those for which they can exist being of a very special form which excludes many space-times generally regarded as significant or interesting. In the present paper I take the matter further and discuss the problem with more generality. It will be shown that the existence of non-trivial regraduations depends firstly upon which theory is being assumed for the derivation of the conservation equations There are two alternatives, and regraduations are found to be excluded by one, the “geodesic” theory, but not necessarily by the other, the “equivalence” theory.

General Relativity

2006 ◽  
Author(s):  
M. P. Hobson ◽  
G. P. Efstathiou ◽  
A. N. Lasenby
Keyword(s):  
General Relativity
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